Prove cos(x+y)*cos(x-y)=cos^2x - sin^2y?

Comments

• sahsjing

  May 2021

  cos(x+y)*cos(x-y)

  = (1/2)[cos(2x) + cos(2y)]

  = (1/2)[2cos^2x - 1 + 1 - 2sin^2y]

  = cos^2x - sin^2y

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  Ideas: 2cosAcosB = cos(A+B) + cos(A-B)
• jay

  May 2021

  cos(x+y)*cos(x-y)=cos^2x - sin^2y

  [cosxcosy - sinxsiny]*[cosxcosy + sinxsiny]

  (cosxcosy)^2 - (sinxsiny)^2

  cos^2xcos^2y - sin^2xsin^2y

  cos^2x(1-sin^2y) - (1-cos^2x)sin^2y

  cos^2x-cos^2xsin^2y-sin^2y+cos^2xsin^2y

  cos^2x-sin^2y => proven